Visa for dependent child

I work in China and my child has, like me, one for Employment. Her passport is about to expire and so her Chinese resident permit. It would be quicker to renew her passport Italy (we are Italian nationals ). What to do to get one as dependant for her in Rome, what document she wil need, and how long it wil take? I will have with me my passport and expert certificate and new Z type valid until next year

Thanks